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alina1380 [7]
3 years ago
11

Find the values of k and b if it is known that the graph of y=kx b goes through points (2, 10) and (−7, −10).

SAT
1 answer:
andreev551 [17]3 years ago
3 0

The values of k and b of this graph that passes through the given points is k = \frac{20}{9}  and b = \frac{-50}{9}

<u>Given the following points:</u>

  • Points on the x-axis = (2, -7)
  • Points on the y-axis = (10, -10)
  • y = kx + b   .....equation 1.

To find the values of k and b since the graph passes through the given points:

First of all, we would determine the slope of the graph passing through the given points.

Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}

Substituting the points into the formula, we have;

Slope. \;m  = \frac{-10 - 10}{-7 - 2}\\\\Slope. \;m  = \frac{-20}{-9}\\\\Slope. \;m  = \frac{20}{9}

The standard form of an equation of line is given by the formula;

y = mx + b   ....equation 2

<u>Where:</u>

  • x and y are the points.
  • m is the slope.
  • b is the intercept.

Next, we would determine the intercept of the graph:

10 = \frac{20}{9}(2) + b\\\\10 =  \frac{40}{9} + b\\\\b =  \frac{40}{9} - 10\\\\b = \frac{40\; - \;90}{9}\\\\b = \frac{-50}{9}

The standard form of this equation of line is:

y = \frac{20}{9}x - \frac{50}{9}    .....equation 3.

Comparing eqn 1 and eqn 3, we can deduce:

k = \frac{20}{9}  and b = \frac{-50}{9}

Therefore, the values of k and b of this graph that passes through the given points is k = \frac{20}{9}  and b = \frac{-50}{9}

Read more: brainly.com/question/18123312

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